Table of contents

Sentinel lymph node biopsy (SLNB), a less invasive alternative to axillary lymph node dissection (ALND), has become the standard of care for patients with clinically node-negative breast cancer. In SLNB, lymphatic mapping with radio-labeled sulfur colloid and/or blue dye helps identify the sentinel lymph node (SLN), which is most likely to contain metastatic breast cancer. Even though SLNB, using both methylene blue and radioactive tracers, has a high identification rate, it still relies on an invasive surgical procedure, with associated morbidity. In this study, we have demonstrated a non-invasive single-walled carbon nanotube (SWNT)-enhanced photoacoustic (PA) identification of SLN in a rat model. We have successfully imaged the SLN in vivo by PA imaging (793 nm laser source, 5 MHz ultrasonic detector) with high contrast-to-noise ratio (=89) and good resolution (∼500 µm). The SWNTs also show a wideband optical absorption, generating PA signals over an excitation wavelength range of 740–820 nm. Thus, by varying the incident light wavelength to the near infrared region, where biological tissues (hemoglobin, tissue pigments, lipids and water) show low light absorption, the imaging depth is maximized. In the future, functionalization of the SWNTs with targeting groups should allow the molecular imaging of breast cancer.

Photoacoustic tomography (PAT) is based on the generation of ultrasound waves by heating an object with short light pulses. A three-dimensional image of the distribution of absorbed energy within the object is reconstructed from signals measured around the object with either point-like or extended, linear sensors. Limited angle artefacts arise when the curve or surface connecting neighbouring detectors is not closed around the object. For this case, there exists a 'detection region' in which all boundaries of an object are visible in the reconstruction. All straight lines passing through each point in this region intersect the detection curve or surface at least once. Although for these points an accurate reconstruction is possible, direct back projection leads to artefacts when some of the straight lines intersect the detection surface twice and others just once. In this work, special weight functions for direct, non-iterative back projection are presented that reduce these kinds of artefacts. A clear improvement in image quality is shown in simulations for three-dimensional (3D) imaging with point detectors and for two-dimensional (2D) imaging using line detectors compared to reconstruction without weight factors. For the 2D case also an experiment is shown. The presented weight factors make commonly used back projection formulae suitable for a more accurate reconstruction of the initial pressure distribution in cases where the detection aperture only covers a limited angle, and the region of interest lies within the detection region.

In recent experiments, quasi-monoenergetic and well-collimated very-high energy electron (VHEE) beams were obtained by laser–plasma accelerators. We investigate their potential use for radiation therapy. Monte Carlo simulations are used to study the influence of the experimental characteristics such as beam energy, energy spread and initial angular distribution on the dose distributions. It is found that magnetic focusing of the electron beam improves the lateral penumbra. The dosimetric properties of the laser-accelerated VHEE beams are implemented in our inverse treatment planning system for intensity-modulated treatments. The influence of the beam characteristics on the quality of a prostate treatment plan is evaluated. In comparison to a clinically approved 6 MV IMRT photon plan, a better target coverage is achieved. The quality of the sparing of organs at risk is found to be dependent on the depth. The bladder and rectum are better protected due to the sharp lateral penumbra at low depths, whereas the femoral heads receive a larger dose because of the large scattering amplitude at larger depths.

It is common, even with new SPECT/CT systems, that the transmission data are truncated. This paper develops a method that obtains exact attenuation correction with truncated transmission data. The emission object (e.g., the heart) is assumed to have a finite, convex support, whose emission projections are not truncated. The transmission measurements over the support are available, but may be truncated outside the support (within the torso). A novel emission data reconstruction technique combines emission projections from conjugate views; a modified version of the ML-EM algorithm is used to reconstruct emission data. The attenuation map outside the support is not needed during reconstruction. The transmission measurements through the support are used to pre-scale the emission data and to reconstruct the attenuation map within the support. The attenuation map reconstruction within the support is an interior problem in which only a biased solution can be obtained using an iterative algorithm. The bias is then corrected by identifying a soft tissue region within the support and the known attenuation coefficient values of these pixels for the soft tissue. Proof of convergence of the new algorithm is provided. Computer simulations verify the accuracy of the new method. Conclusions: an exact attenuation map within the support can be obtained provided the attenuation coefficient is known at 1 pixel within the support. The method, which requires emission data over 360°, provides a means to perform attenuation correction in SPECT with truncated transmission data.

Recent studies of the minute morphology of the skin by optical coherence tomography revealed that the sweat ducts in human skin are helically shaped tubes, filled with a conductive aqueous solution. This, together with the fact that the dielectric permittivity of the dermis is higher than that of the epidermis, brings forward the supposition that as electromagnetic entities, the sweat ducts could be regarded as low Q helical antennas. The implications of this statement were further investigated by electromagnetic simulation and experiment of the in vivo reflectivity of the skin of subjects under varying physiological conditions (Feldman et al 2008 Phys. Rev. Lett. 100 128102). The simulation and experimental results are in a good agreement and both demonstrate that sweat ducts in the skin could indeed behave as low Q antennas. Thus, the skin spectral response in the sub-Terahertz region is governed by the level of activity of the perspiration system and shows the minimum of reflectivity at some frequencies in the frequency band of 75–110 GHz. It is also correlated to physiological stress as manifested by the pulse rate and the systolic blood pressure. As such, it has the potential to become the underlying principle for remote sensing of the physiological parameters and the mental state of the examined subject.

Volumetric CT imaging systems usually comprise a point x-ray source and a 2D detector. Flat panel imager (FPI)-based cone beam CT (CBCT) has become an important online imaging modality for image-guided radiotherapy and intervention. However, due to excessive scatter photons and inferior detector performance, the image quality of current CBCT is significantly inferior to diagnostic fan-beam CT. We propose a novel tetrahedron beam computed tomography (TBCT) imaging system which consists of a linear scan x-ray source and a linear x-ray detector array. The linear x-ray tube and detector array are aligned perpendicular and parallel to the rotation plane, respectively. The x-ray beams are narrowly collimated into fan beams and focused on the linear detector array. The linear detector and linear x-ray source form a 'tetrahedron' volume instead of a 'cone' volume. TBCT is similar to CBCT in image reconstruction geometry; however, its image quality will be significantly superior to that of CBCT due to its scatter rejection mechanism and the use of high-performance discrete x-ray detectors. In this paper, we describe the design of the TBCT system for image-guided radiotherapy and some results of preliminary studies.

We have investigated the feasibility and accuracy of using a combination of internal and external fiducials for respiratory-gated image-guided radiotherapy of liver tumors after screening for suitable patients using a mock treatment. Five patients were enrolled in the study. Radio-opaque fiducials implanted adjacent to the liver tumor were used for daily online positioning using either electronic portal or kV images. Patient eligibility was assessed by determining the degree of correlation between the external and internal fiducials as analyzed during a mock treatment. Treatment delivery was based on the modification of conventional amplitude-based gating. Finally, the accuracy of respiratory-gated treatment using an external fiducial was verified offline using the cine mode of an electronic portal imaging device. For all patients, interfractional contribution to the random error was 2.0 mm in the supero-inferior direction, which is the dominant direction of motion due to respiration, while the interfractional contribution to the systematic error was 0.9 mm. The intrafractional contribution to the random error was 1.0 mm. One of the significant advantages to this technique is improved patient set-up using implanted fiducials and gated imaging. Daily assessment of images acquired during treatment verifies the accuracy of the delivered treatment and uncovers problems in patient set-up.

This paper presents finite-difference time-domain (FDTD) calculations of specific absorption rate (SAR) values in the head under plane-wave exposure from 1 to 10 GHz using a resolution of 0.5 mm in adult male and female voxel models. Temperature rise due to the power absorption is calculated by the bioheat equation using a multigrid method solver. The computational accuracy is investigated by repeating the calculations with resolutions of 1 mm and 2 mm and comparing the results. Cubically averaged 10 g SAR in the eyes and brain and eye-averaged SAR are calculated and compared to the corresponding temperature rise as well as the recommended limits for exposure. The results suggest that 2 mm resolution should only be used for frequencies smaller than 2.5 GHz, and 1 mm resolution only under 5 GHz. Morphological differences in models seemed to be an important cause of variation: differences in results between the two different models were usually larger than the computational error due to the grid resolution, and larger than the difference between the results for open and closed eyes. Limiting the incident plane-wave power density to smaller than 100 W m⁻² was sufficient for ensuring that the temperature rise in the eyes and brain were less than 1 °C in the whole frequency range.

The purpose of this study was to evaluate the feasibility of using localized harmonic motion (LHM) to monitor and control focused ultrasound surgery (FUS) in VX2 tumors in vivo. FUS exposures were performed on 13 VX2 tumors implanted in nine rabbits. The same transducer induced coagulation and generated a localized oscillatory motion by periodically varying the radiation force. A separate diagnostic ultrasound transducer tracked motion by cross-correlating echo signals at different instances. A threshold in motion amplitude was instituted to cease exposure. Coagulation was confirmed by T2-weighted MR images, thermal dose obtained through MR thermometry and histological examinations. For tumor locations achieving coagulation, the LHM amplitude was 9% (p = 0.04) to 57% (p < 0.0001) lower than that before exposure. Control was successful for 74 (69%) out of 108 cases, with 52 (48%) reaching the threshold and achieving coagulation and 22 (21%) never reaching threshold nor coagulating. For the 34 (31%) unsuccessful exposures, 16 (15%) never reached the threshold but coagulation occurred, and 18 (16%) reached threshold without coagulation confirmed. Noise or radio-frequency signal changes explained motion over- or underestimation in 24 (22%) cases; the remaining 10 (9%) had other causes of error. The control was generally successful, but sudden change or noise in the acquired echo signal caused failure. Coagulation after exposure could be validated by comparing amplitudes before and after exposure.

All radiation therapy treatment planning relies on accurate dose calculation. Uncertainties in dosimetric prediction can significantly degrade an otherwise optimal plan. In this work, we introduce a robust optimization method which handles dosimetric errors and warrants for high-quality IMRT plans. Unlike other dose error estimations, we do not rely on the detailed knowledge about the sources of the uncertainty and use a generic error model based on random perturbation. This generality is sought in order to cope with a large variety of error sources. We demonstrate the method on a clinical case of lung cancer and show that our method provides plans that are more robust against dosimetric errors and are clinically acceptable. In fact, the robust plan exhibits a two-fold improved equivalent uniform dose compared to the non-robust but optimized plan. The achieved speedup will allow computationally extensive multi-criteria or beam-angle optimization approaches to warrant for dosimetrically relevant plans.

We present three novel multi-slit-slat (MSS) system designs which allow for the acquisition of data with variable multiplexing in order to optimize the use of a high intrinsic resolution detector for clinical brain SPECT. In this paper we first study the relationship between the geometric parameters of a MSS collimator system and the resulting resolution and sensitivity for an on-axis point at the centre of the field-of-view (FOV), assuming a continuous cylindrical detector model. The model predicts that for optimal system sensitivity and resolution, the ratio of the detector radius to slit collimator radius should be 1.3–1.5, as any further increase in this ratio results in significant deterioration in both system resolution and sensitivity. The analytical results were used to fix the geometric parameters for the three novel MSS system designs. Comparison of the three designs, asymmetric rotating collimator (ARC), asymmetric rotating detector (ARD) and symmetric rotating collimator (SRC) with variable slit spacing, suggests that the SRC system performs better in terms of the system sensitivity (5.1 × 10⁻⁴) for the same average resolution (6.0 mm) in comparison to designs based on an ARC (3.7 × 10⁻⁴) and ARD (4.2 × 10⁻⁴).

The electronic stopping power of liquid water for protons over the 50 keV to 10 MeV energy range is studied using an improved dielectric response model which is in good agreement with the best available experimental data. The mean excitation energy (I) of stopping power theory is calculated to be 77.8 eV. Shell corrections are accounted for in a self-consistent manner through analytic dispersion relations for the momentum dependence of the dielectric function. It is shown that widely used dispersion schemes based on the random-phase approximation (RPA) can result in sizeable errors due to the neglect of damping and local field effects that lead to a momentum broadening and shifting of the energy-loss function. Low-energy Born corrections for the Barkas, Bloch and charge-state effects practically cancel out down to 100 keV proton energies. Differences with ICRU Report 49 stopping power values and earlier calculations are found to be at the ∼20% level in the region of the stopping maximum. The present work overcomes the limitations of the Bethe formula below 1 MeV and improves the accuracy of previous calculations through a more consistent account of the dielectric response properties of liquid water.

Intensity inhomogeneities in magnetic resonance images (MRI) are a frequently occurring artefact, and result in the same tissue class to have vastly different intensities within an image. These inhomogeneities can be modelled by a slowly varying field, which is also called the bias field. Previous phantom-, image- or sequence based approaches suffer from long scan times, post-processing times or do not sufficiently remove the intensity variations. These intensity variations cause problems for quantitative image analysis algorithms (segmentation, registration) as well as clinicians (e.g. by complicating the visual assessment). This paper presents a novel technique (COIN, correction of intensity inhomogeneities) that uses two calibration images (fast spoiled gradient echo) to map a parameter containing the bias field, which is specific to the patient during a particular exam. This parametric map can then be used to correct any other images acquired during the same exam, regardless of the sequence employed. By using a short repetition time (less than 5 ms) for the calibration scans, the additional scan time is reduced to 60 s (max). The subsequent post-processing time is approximately 60 s per 20 slices. We successfully validate our approach on simulated brain MRI as well as real liver and spinal images. These images were acquired with a number of different coils, sequences and weightings. A comparison of our method with an existing, commercially available algorithm by radiologists shows that COIN is superior.

Intraoperative electron beam radiotherapy (IOERT) is a technique in which a single-fraction high dose is intraoperatively delivered to subclinical tumour cells using an electron beam after breast-conserving surgery. In IOERT, an attenuation plate consisting of a pair of metal disks is commonly used to protect the normal tissues posterior to the breast. However, the dose in front of the plate is affected by backscatter, resulting in an unpredictable delivered dose to the tumour cells. In this study, an experimental attenuation plate, termed a shielding plate, was designed using Monte Carlo simulation, which significantly diminished the electron beam without introducing any backscatter radiation. The plate's performance was verified by measurements. It was made of two layers, a first layer (source side) of polymethyl methacrylate (PMMA) and a second layer of copper, which was selected from among other metals (aluminium, copper and lead) after testing for shielding capability and the range and magnitude of backscatter. The optimal thicknesses of the PMMA (0.71 cm) and copper (0.3 cm) layers were determined by changing their thicknesses during simulations. On the basis of these results, a shielding plate was prototyped and depth doses with and without the plate were measured by radiophotoluminescence glass dosimeters using a conventional stationary linear accelerator and a mobile linear accelerator dedicated for IOERT. The trial shielding plate functioned as intended, indicating its applicability in clinical practice.

Silicon photomultipliers (SiPMs) are of great interest to positron emission tomography (PET), as they enable new detector geometries, for e.g., depth-of-interaction (DOI) determination, are MR compatible, and offer faster response and higher gain than other solid-state photosensors such as avalanche photodiodes. Here we present a novel detector design with DOI correction, in which a position-sensitive SiPM array is used to read out a monolithic scintillator. Initial characterization of a prototype detector consisting of a 4 × 4 SiPM array coupled to either the front or back surface of a 13.2 mm × 13.2 mm × 10 mm LYSO:Ce³⁺ crystal shows that front-side readout results in significantly better performance than conventional back-side readout. Spatial resolutions <1.6 mm full-width-at-half-maximum (FWHM) were measured at the detector centre in response to an ∼0.54 mm FWHM diameter test beam. Hardly any resolution losses were observed at angles of incidence up to 45°, demonstrating excellent DOI correction. About 14% FWHM energy resolution was obtained. The timing resolution, measured in coincidence with a BaF₂ detector, equals 960 ps FWHM.

This paper describes the potential application of an active pixel sensor-based x-ray diffraction (APXRD) system in the field of breast cancer diagnosis. The design and initial testing of the system was reported previously (Bohndiek et al 2008b Phys. Med. Biol.53 655–72). The system has potential both as a 'diffraction enhanced breast imager' (DEBI) and as a probe for quantitative analysis of breast biopsy samples. The resolution of the system in a DEBI arrangement is 1 mm and the contrast available using a material-specific x-ray diffraction image was found to be up to seven times greater than that of a transmission image. Scatter signatures from a series of biopsy-equivalent samples, ranging in composition from 100% fat to 100% fibrous tissue, were acquired with the APXRD system. Multivariate data analysis was used to produce a partial least squares (PLS) model sensitive to sample fat content. The final model is able to accurately predict the fat content of a series of unknown samples and is robust to significant added noise. This suggests that the APXRD system could provide a simple, semi-automated, quantitative measurement system for analysis of breast biopsy samples. Training on a range of scatter signatures from real breast biopsy samples covering various stages of disease is now needed to test this hypothesis.

Lung tumor motion due to respiration poses a challenge in the application of modern three-dimensional conformal radiotherapy. Direct tracking of the lung tumor during radiation therapy is very difficult without implanted fiducial markers. Indirect tracking relies on the correlation of the tumor's motion and the surrogate's motion. The present paper presents an analysis of the correlation between tumor motion and diaphragm motion in order to evaluate the potential use of diaphragm as a surrogate for tumor motion. We have analyzed the correlation between diaphragm motion and superior–inferior lung tumor motion in 32 fluoroscopic image sequences from ten lung cancer patients. A simple linear model and a more complex linear model that accounts for phase delays between the two motions have been used. Results show that the diaphragm is a good surrogate for tumor motion prediction for most patients, resulting in an average correlation factor of 0.94 and 0.98 with each model respectively. The model that accounts for delays leads to an average localization prediction error of 0.8 mm and an error at the 95% confidence level of 2.1 mm. However, for one patient studied, the correlation is much weaker compared to other patients. This indicates that, before using diaphragm for lung tumor prediction, the correlation should be examined on a patient-by-patient basis.

Intensity-modulated arc therapy (IMAT) is a rotational variant of intensity-modulated radiation therapy (IMRT) that can be implemented with or without angular dose rate variation. The purpose of this study is to assess optimization strategies and initial conditions using a leaf position optimization (LPO) algorithm altered for variable dose rate IMAT. A concave planning target volume (PTV) with a central cylindrical organ at risk (OAR) was used in this study. The initial IMAT arcs were approximated by multiple static beams at 5° angular increments where multi-leaf collimator (MLC) leaf positions were determined from the beam's eye view to irradiate the PTV but avoid the OAR. For the optimization strategy, two arcs with arc ranges of 280° and 150° were employed and plans were created using LPO alone, variable dose rate optimization (VDRO) alone, simultaneous LPO and VDRO and sequential combinations of these strategies. To assess the MLC initialization effect, three single 360° arc plans with different initial MLC configurations were generated using the simultaneous LPO and VDRO. The effect of changing optimization degrees of freedom was investigated by employing 3°, 5° and 10° angular sampling intervals for the two 280°, two 150° and single arc plans using LPO and VDRO. The objective function value, a conformity index, a dose homogeneity index, mean dose to OAR and normal tissues were computed and used to evaluate the treatment plans. This study shows that the best optimization strategy for a concave target is to use simultaneous MLC LPO and VDRO. We found that the optimization result is sensitive to the choice of initial MLC aperture shapes suggesting that an LPO-based IMAT plan may not be able to overcome local minima for this geometry. In conclusion, simultaneous MLC leaf position and VDRO are needed with the most appropriate initial conditions (MLC positions, arc ranges and number of arcs) for IMAT.

A target-tracking, intensity-modulated delivery on an Elekta MLCi system was assessed by film measurement with a simulated target–motion trajectory. A toroidally shaped idealized target surrounding an organ at risk necessitating multiple field segments to irradiate the target and spare the organ at risk was defined in a solid-water phantom. The phantom was programmed to move following a reproducible 2D elliptical trajectory in the beam's-eye view with a period of 10 s. Static and target-tracking treatments were planned for delivery on a standard Elekta Precise series linac with integrated MLCi system. Dose was delivered in three ways: (i) a static treatment to a static phantom, (ii) a static treatment to a moving phantom and (iii) a target-tracking treatment to a moving phantom. The dose delivered was assessed by film measurement on the central plane through the target and organ at risk. The target dose blurring was quantified by the standard deviation of the dose to the target which was evaluated as 2.8% for the static treatment to the static phantom, 7.2% for the static treatment to the moving phantom and 2.6% for the tracking treatment to the moving phantom. The mean organ-at-risk dose was 38.2%, 54.0% and 38.2% of the prescription dose for each delivery case. We have therefore shown that the linac is capable of delivering target-tracking fields with MLCs for the target trajectories tested.

Quantifying the mechanical properties of soft tissues remains a challenging objective in the field of elasticity imaging. In this work, we propose an ultrasound-based method for quantitatively estimating viscoelastic properties, using the amplitude-modulated harmonic motion imaging (HMI) technique. In HMI, an oscillating acoustic radiation force is generated inside the medium by using focused ultrasound and the resulting displacements are measured using an imaging transducer. The proposed approach is a two-step method that uses both the properties of the propagating shear wave and the phase shift between the applied stress and the measured strain in order to infer to the shear storage (G') and shear loss modulus (G''), which refer to the underlying tissue elasticity and viscosity, respectively. The proposed method was first evaluated on numerical phantoms generated by finite-element simulations, where a very good agreement was found between the input and the measured values of G' and G''. Experiments were then performed on three soft tissue-mimicking gel phantoms. HMI measurements were compared to rotational rheometry (dynamic mechanical analysis), and very good agreement was found at the only overlapping frequency (10 Hz) in the estimate of the shear storage modulus G' (14% relative error, averaged p-value of 0.34), whereas poorer agreement was found in G'' (55% relative error, averaged p-value of 0.0007), most likely due to the significantly lower values of G'' of the gel phantoms, posing thus a greater challenge in the sensitivity of the method. Nevertheless, this work proposes an original model-independent ultrasound-based elasticity imaging method that allows for direct, quantitative estimation of tissue viscoelastic properties, together with a validation against mechanical testing.

This study introduces a new approach for the application of principal component analysis (PCA) with pre-normalization on dynamic positron emission tomography (PET) images. These images are generated using the amyloid imaging agent N-methyl [¹¹C]2-(4'-methylaminophenyl)-6-hydroxy-benzothiazole ([¹¹C]PIB) in patients with Alzheimer's disease (AD) and healthy volunteers (HVs). The aim was to introduce a method which, by using the whole dataset and without assuming a specific kinetic model, could generate images with improved signal-to-noise and detect, extract and illustrate changes in kinetic behavior between different regions in the brain. Eight AD patients and eight HVs from a previously published study with [¹¹C]PIB were used. The approach includes enhancement of brain regions where the kinetics of the radiotracer are different from what is seen in the reference region, pre-normalization for differences in noise levels and removal of negative values. This is followed by slice-wise application of PCA (SW-PCA) on the dynamic PET images. Results obtained using the new approach were compared with results obtained using reference Patlak and summed images. The new approach generated images with good quality in which cortical brain regions in AD patients showed high uptake, compared to cerebellum and white matter. Cortical structures in HVs showed low uptake as expected and in good agreement with data generated using kinetic modeling. The introduced approach generated images with enhanced contrast and improved signal-to-noise ratio (SNR) and discrimination power (DP) compared to summed images and parametric images. This method is expected to be an important clinical tool in the diagnosis and differential diagnosis of dementia.

The 'sub-millimetre precision' often claimed to be achievable in protons and light ion beam therapy is analysed using the Monte Carlo code SHIELD-HIT for a broad range of energies. Based on the range of possible values and uncertainties of the mean excitation energy of water and human tissues, as well as of the composition of organs and tissues, it is concluded that precision statements deserve careful reconsideration for treatment planning purposes. It is found that the range of I-values of water stated in ICRU reports 37, 49 and 73 (1984, 1993 and 2005) for the collision stopping power formulae, namely 67 eV, 75 eV and 80 eV, yields a spread of the depth of the Bragg peak of protons and heavier charged particles (carbon ions) of up to 5 or 6 mm, which is also found to be energy dependent due to other energy loss competing interaction mechanisms. The spread is similar in protons and in carbon ions having analogous practical range. Although accurate depth–dose distribution measurements in water can be used at the time of developing empirical dose calculation models, the energy dependence of the spread causes a substantial constraint. In the case of in vivo human tissues, where distribution measurements are not feasible, the problem poses a major limitation. In addition to the spread due to the currently accepted uncertainties of their I-values, a spread of the depth of the Bragg peak due to the varying compositions of soft tissues is also demonstrated, even for cases which could be considered practically identical in clinical practice. For these, the spreads found were similar to those of water or even larger, providing support to international recommendations advising that body-tissue compositions should not be given the standing of physical constants. The results show that it would be necessary to increase the margins of a clinical target volume, even in the case of a water phantom, due to an 'intrinsic basic physics uncertainty', adding to those margins usually considered in normal clinical practice due to anatomical or therapeutic strategy reasons. Individualized patient determination of tissue composition along the complete beam path, rather than CT Hounsfield numbers alone, would also probably be required even to reach 'sub-centimetre precision'.

A simple analytical model is developed that allows efficient absolute dose reconstruction in patients undergoing radiation treatments using proton beams. The model is based on the solution of the inverse problem of dose recovery from the 3D information contained in the PET signal, obtained immediately after the treatment. The core of the proposed model lies in the analytical calculation of the introduced positron emitters' species matrix (PESM) or kernel, facilitated by previously developed theoretical calculations of the proton energy fluence distribution. Once the PESM is known, the absolute dose distribution in a patient can be found from the deconvolution of the 3D activity distribution obtained from the PET scanner with the calculated species matrix. As an example, we have used FLUKA Monte Carlo code to simulate the delivery of the radiation dose to a tissue phantom irradiated by a parallel-opposed beam arrangement and calculated the resultant total activity. Deconvolution of the calculated activity with the PESM leads to the reconstructed dose being within 2% of that delivered.